Using (REF ) and (REF ), we conclude from Theorem REF  that the inner \(\alpha \) -Riesz equilibrium measure \(\gamma _A\)  has finite energy if and only if \(c_\alpha (A)<\infty \) ; and in the affirmative case it can alternatively be characterized, for instance, as the only measure in \(\mathcal {E}^{\prime }_A\)  having the property \(\kappa _\alpha \gamma _A=1\)  n.e. \(A\) . Regarding the latter, see [1]}.
